6 Answers
6

The best you can do is get the fastest DDR3 which the system will support. I can't find anything specific about the fastest you can use in the Asus EEE PC 1015PEM but I did find a few laptops using DDR3 1066 ram.

Newegg's memory finder lists modules up to DDR3 1333 (http://www.newegg.com/MemoryFinder/#y8wBAbp0ad0ABD) for all the included Asus Eee PC 1015* notebook's (up to 1666 for a few of them) but there is no listing for the 1015PEM. Of course the price difference is minimal for trusted brands like Kingston and there is no downside to using RAM which is too fast for the system, it will simply run at a slower speed.

Of course, the real limit is the processor and the demands of Win7. Try disabling all Aero fetures and any other "eye-candy" if you haven't already. If you're adventurous you may see noticeable gains from using a lightweight linux distro.

according to you net-book model from here, there is only one DDR3 SO-DIMM memory slot that Asus Pre-installed with 1x1gb module, you can change it to 1x2gb DDR3 module. I'm not sure about installing 4gb module on this model. because they make hard coded limitation on net-book main-board for this kind of upgrade.
and because of that there is no need to upgrade to 64bit of windows.

Generally speaking,
you can run Windows Experience Index, look at the lowest scores results and upgrade whatever is upgradable.

Specifically speaking, the Asus EEE PC 1015P EM buttole neck is the very slow hard drive.
I replaced the hard drive with an SSD hard drive. I still have 1GB ram (will upgrade to 2GB soon) and the difference in the computer speed is unbelievable!
It actually works and responds like a normal computer should.